Resurgence Corrections for Non-Holomorphic Fractal Families: Exact Class B′ Hypergeometric Identification and Transfer Lemma

Paper 8 asserted a universal square-root Borel branch point at s = 1 for all pure-power-law classes (A, B′, C) of the Bird non-holomorphic fractal classification, and left three structural gaps: no uniform proof mechanism, an unverified Class B′ hypergeometric identification, and no independent analysis of Class A’s asymptotic variable. This paper closes the first two gaps and provides a structural observation on the third. Class B′ (main result). The Poincaré coefficient sequence D_n^{B′} from Paper 8 has generating function G^{B′}(s) = (π / α sin(π/α)) · ₂F₁(1/2, 1/α; 1; s), an exact Gauss hypergeometric identity proved by Pochhammer expansion. The local exponent at s = 1 is μ(α) = 1/2 − 1/α, which varies…